Effective temperature. To distinguish between different social phases, we implement tools from statistical physics to explore a central thermodynamic quantity, temperature \(T\) . The Stokes-Einstein relation \(k_BT=D\zeta \)  relates temperature in Brownian motion to the diffusion constant \(D\)  and viscosity \(\zeta \) . For interactive systems, the Stokes-Einstein relation has been generalized as the fluctuation-dissipation theorem [1]}, [2]}. To find diffusion constant \(D\) , we first measure the mean square displacement (MSD), \(\langle \Delta r^2\rangle \) , that quantifies the variance of individual movements over time \(t\) . For two-dimensional Brownian motion, the MSD scales linearly with time as \(\langle \Delta r^2\rangle = 4Dt\) , where the slope is proportional to the diffusion constant \(D\) . Figure 2a-c plots averaged MSD for datasets D1-D2, showing a linear dependency at a short time scale \(t\ll \tau _s\) , where \(\tau _s\)  represents a typical time scale for social interaction. We find that \(\tau _s\approx 3s\)  for datasets D1A-D1B, whereas the MSD in D2 does not show this typical diffusion regime, due to experimental limitation of temporal resolution (see SM Section B2). In the continuation of \(\langle \Delta r^2\rangle \) , \(t\gg \tau _s\) ; that is, individuals diffuse sub-linearly, as \(\langle \Delta r^2\rangle \sim t^{\alpha }\) . The exponent \(\alpha \approx 0.3\sim 0.5\)  (see SM Section B2) indicates a slowdown in movement due to social interaction. We measure the diffusion constant \(D\)  for D1-D2 (see SM Section B2), finding that the D2 dataset has the largest diffusion constant.
